Dynamical behavior of similarity solutions of CKOEs with conservation law

New variable separation solutions and localized waves for (2+1)-dimensional nonlinear systems by a full variable separation approach

“…Searching different exact solutions for various nonlinear waves and then exploring their dynamics is always an important and interesting issue [26,27,43]. It is obvious that the new full variable separation solutions of the BLMP, NNV and DLW equations contain some arbitrary one dimensional functions with respect to x, y and t, respectively.…”

Dynamics of invariant solutions of mKdV-ZK arising in a homogeneous magnetised plasma

“…With repeated use of Lie symmetry reduction, the (3 + 1)-mKdV-ZK reduces to an ODE, which is much easier to solve. The brief description and applications of the method can be studied from some text books [22,23] and references therein [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Assuming one-parameter Lie group of the following transformations…”

Some invariant solutions of coupled Konno-Oono equations arising in electromagnetic and quantum fields

“…There is no simple way to obtain an explicit solution to a nonlinear system, therefore, some well-known approaches, such as ISM [1,6,7], Classical Lie symmetry [9], Optimal subalgebra using Lie symmetry [10],…”

“…Finally he [9] obtained a kink type solution. Authors [10] employed optimal subalgera classification with Killing form to provide invariants for the same form of the CKOEs (1) and obtained a new class of solutions. Different particular forms of the CKOEs were solved by a community of researchers like Abul Bashar et al [12] as well as Khan and Akbar [13] derived traveling wave solutions of CKOEs (3).…”

“…Because such solutions are helpful in explain PDEs physical behavior. Authors are motivated by the above literature [9][10][11][12][13][14][15][16][17][18][19][20][21] covering different forms of CKOEs (1) to solve it analytically.…”